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Some limit laws for strongly additive prime indicators. (English) Zbl 1163.11058

The authors consider convergence to some weak limit law for distributions \[ \nu_x(f_x(n)< u)={1\over [x]} \sum_{\substack{ n\leq x\\ f_x(n)< u}} 1, \] where the \(f_x\) are strongly additive functions, \(x\geq 2\), and \(f_x(p)\) is \(0\) or \(1\) for every prime \(p\). As limit laws there are investigated the Poisson, Bernoulli, binomial, geometrical distributions and some mixtures of them.

MSC:

11K65 Arithmetic functions in probabilistic number theory
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